In a dining establishment in Lyon, you can eat pig fat fried in pig fat, a pig's brain dressed in a porky vinaigrette, a salad made with creamy pig lard, a chicken cooked inside a sealed pig's bladder, a pig's digestive tract filled up with pig's blood and cooked like a custard, nuggets of a pig's belly mixed with cold vinegary lentils, a piggy intestine blown up like a balloon and stuffed thickly with a handful of piggy intestines, and a sausage roasted in a brioche (an elevated version of a "pig in a blanket"). For these and other reasons, Lyon, for 76 years, has been recognised as the gastronomic capital of France and the world. The world is a big place. Two and a half years ago, I persuaded my wife Jessica Green and our three-year-old twins that we should move to Lyon to see what was so good about the good food there.

Should I have proposed a two-week holiday? We had been happy in New York, in an apartment by a park. We had neighbours. We had friends. But, for reasons I didn't understand, I felt I needed to learn how to cook the food of France and knew that I was going to have to get over to the country: to Paris, I'd always assumed. But where in Paris, and doing what? I interrogated chefs, including Daniel Boulud, whom I tracked down on a family vacation, and the great Michel Richard, whom I met on a train from Washington DC.

They all said: Go to Lyon.

Lyon? Who goes to Lyon?

We arrived at the end of 2008.

We found a flat. It had no oven. The windows didn't shut. It was cold. Bits of semi-frozen Rhone Valley river scum floated into our lungs and infected them with microscopic bronchial suicide bombers. We went to A&E. We got lice. We got lice again. One of our children walked on a taxi seat in his tiny three-year-old shoes; the driver hit him with his fist. I swore at the driver. He thanked me. I swore at myself. Why did I think I spoke French? The plan had been to stay six months. What about six days? Six days passed. Six months passed. Did we forget to leave? We are in our third year. We have no exit strategy. Is Lyon the world's gastronomic capital – is that why we're still here? This is what we've discovered.

BEST LYONNAIS MEAL

Lunch. Small price, big bang: simple, never fancy, like the food you wish your mother had cooked, and so cheap that, even with wine, even with a lot of wine, even with a ridiculous amount of wine, you'll stare at l'addition looking for the mistake. Best version? Anywhere. Everywhere. There will be one expensive item: the espresso, unfortunate because it tastes of mud.

WORST LYONNAIS MEAL

Breakfast. Tip: if staying the night, pack a cup of coffee.

BEST-VALUE KILLER MEAL

Saisons, the inexplicably elegant establishment on the ground floor of a 19th-century silk-maker's preposterous folly – towers, turrets, there must have been a moat – otherwise known as L'Institut Paul Bocuse, in Ecully, four miles away: yes, a cooking school. (In Lyon, every food institution is named Paul Bocuse.) The kitchen is run by Alain le Cossec. Nota bene: Alain le Cossec, MOF (1991), chef, icy Zen master of culinary perfection, is not a student. You don't go to a restaurant, especially in Lyon, to support amateurs making a mess of your dinner. The secret: no student is allowed close to the food. (How do I know? I became a student.)

BEST SATURDAY NIGHT BOUCHON

BEST SUNDAY NIGHT BOUCHON

Bouchon des Filles. Run by two sisters and former waitresses of Café des Fédérations. They describe their place as a bouchon run by women for people who think that a normal bouchon is too heavy. Me? I describe it as good.

BEST BOUCHON ANYTIME

Daniel et Denise, except it's not a bouchon, it's a restaurant that just happens to serve classic Lyonnais dishes done so expertly that you don't recognise them as classic Lyonnais dishes. The chef, who is neither a Daniel nor a Denise but a Joseph, is another MOF. (An MOF is a Meilleur Ouvrier de France; it's French for "I'm kick-ass, you're not" although, to preserve the force of the abbreviation, the best English translation might be 'MOther Fucker'). Chef Joseph Viola became an MOF in 2004, just before buying Daniel et Denise from Daniel and Denise and quitting his job as chef of the once famous Lyon de Lyon, where you could eat classic Lyonnais dishes done so expertly that only a Michelin inspector could spot them. Lyon de Lyon hasn't seen a Michelin inspector for some time.

BEST SMALL RESTAURANT YOU HAVEN'T HEARD OF AND WHERE YOU WON'T GET A RESERVATION

BEST BREAD

Bob's (even Bob doesn't remember why people call him Bob when his name is Yves). On the Quai Saint-Vincent. Old-fashioned, pre-revolutionary bread. Go there. Eat. You will understand why the French once put away three kilos of the stuff a day. The boulangerie was my first apprenticeship, dragging my sorry ass out of my warm matrimonial bed at four in the cold morning, bundling up, the city in deep sleep, then unbundling in front of the hot ovens, trying to figure out the sweet secret of Bob's bread. He said: the flour. I wondered: the water? I concluded: touch (that yeasty buoyancy) and timing (to get crunch and softness). If I spent three more years with Bob, I'd nail it.

BEST OLD-FASHIONED QUENELLE

At Café Comptoir Abel. Neither a café nor a comptoir but a bouchon with an excess of atmosphere so precious that even Daniel Boulud has admitted to a scheme to steal it. Abel's chef, Alain Vigneron, is the only person still standing behind a stove who knows how to make a quenelle as it was done 76 years ago. A quenelle is less a recipe than a clever invention that, in Vigneron's preparation, renders a bony, virtually inedible Rhone lake fish into a creamy soufflé-like poem irritatingly evocative of sex. In fact, it's not Vigneron's preparation; he stole it from the grave of Eugenie Brazier, aka Mère Brazier, France's first woman to get three Michelin stars. Today you still see (on the wall of restaurants where she never worked, at the tabac, on a bus), not just her picture, but the picture, the now-iconic image that was taken in 1935 by Theo Blanc and Antoine Demilly, the Lyonnais celebrity photo team, that depicts a tough, rotund, no-nonsense woman in a too-tight chef's garb, stirring a steamy, unexplained pot with demonic intensity. I learned these things working at Abel, trying to master the quenelle. I failed. I can't do the pointy egg-shape operation with two spoons, although rarely a day passes when I don't try: with my children's ice cream, the morning yoghurt, once with my toothpaste.

BEST POSTMODERN QUENELLE

A confection, lighter than the sea, marginally heavier than air, and with the mouth-feel of a cloud that was presented to the world at 11.45am on 5 April, 2010. At La Mère Brazier: the restaurant, not the person, who had died in 1977, by which time the place had been run for more than a decade by her son, the parent and progeny having developed such a loathing that she abandoned both kitchen and child, opened another establishment in the countryside, and became the world's first six-star chef. When the son died, his daughter, Jacotte, took over, and, in time, sold up to Mathieu Viannay has been reinventing Mère Brazier's recipes ever since, although it took 18 months to come up with a postmodern quenelle. Viannay became an MOF in 2004. Like the other MOFs, he wears a collar that's a version of the French flag and which makes you feel that you should stand at attention whenever he enters the room, which is what his cooks do, then stare longingly at his MOF neckwear, muttering that one day, they, too, will grow up to be an MOF. (Source? Me. I worked there six months.)

BEST PLACE AT DAWN ON SUNDAY

The Roman amphitheatre. You have no idea.

BEST PLACE AT MIDNIGHT

The amphitheatre of the Trois Gaules, the world's first pub. Early Christians were skinned alive. The first, Blandine, was a teenager and a saint. People still report wailing at night.

BEST RESTO I HAVEN'T EATEN AT

Régis et Jacques Marcon, in Saint-Bonnet-le-Froid, a village of 252 people, in high, white-pine woody mountains, an hour-plus drive southwest of Lyon. Régis is the dad; Jacques the son, both born in the village, although the father has additional distinctions of having been born in the home where he was conceived (then also a bistro, run by his mother) and of being given the most local of local names, Régis, after Saint Régis, who died in Lalouvesc, two hours away by foot, in 1640. On a hot summer, 335 years later, Régis, then 19, visited Lalouvesc (with 503 people, the big town), stayed long enough to meet a 16-year-old named Michèle, returned home betrothed, and hasn't left Saint-Bonnet-le-Froid since, except to collect the occasional trophy, including, in 1995, a gold replica of the oblong Paul Bocuse, awarded to the winner of the Bocuse d'Or, the biennial cook-off honouring the country making the best French food. [for Rachel Cooke's report from the 2011 event turn to page 38.] This much I knew last June, when I booked a table for a Wednesday, not knowing that I'd got my reservation so easily because there are no mushrooms in June. I didn't know much more when I had to cancel, or when I phoned back two months later, and learned that there were no tables for three months. What I didn't understand was the French system of controlled branding (affectionately known as the Appellation Controllée), which ensures that one town, and no other, has the one thing you want. Your good lentils come from Puy. Your prunes? Agen. Your pepper from Espelette, your beans from Tarbes, your chickens from Bresse, and your wild mushrooms (who knew?) from Saint-Bonnet-le-Froid. On a single Saturday last November, the village saw 20,000 visitors, all afflicted with an appetite for mushrooms. I know because I phoned the restaurant on that day of all days, still hoping for a cancellation. It had none. Then it closed for four months. Who picks mushrooms in the snow?

BEST BOUTIQUE HOTEL IN LYON

None.

WHY LYON?

Because of what's not in Lyon but nearby. The food-makers, like Régis Marcon and his son, or Alain Chapel, 15 miles east, now run by his son (and where Heston Blumenthal fattened his first ducks), or Le Pyramide, 15 miles south, where Paul Bocuse learned how to cook with a pig's bladder, or Marc Veyrat (and his disciple Emmanuel Renant), both in the Alpine foothills, both cuisiniers of the dirt clod (who needs foie gras when you have wild pasture weeds peed on by a Beaufort cow?). And because of what is grown in the dirt itself. Amid the dormant volcanoes north of Lyon: that's Beaujolais. Ten minutes further in a car: Macon, where the white grapes start. Another hour: Burgundy. And in the other direction, tilting from the impossibly steep hills overlooking the Rhone: that's Côte Rôtie. And the rows of white clusters, mixed in amid the syrah: that's the stressed, struggling, perfumed viognier grapes of Condrieu. Sommeliers hold to the implicit belief that a wine complements food; that, in effect, the food comes first. ("You're having the sole, sir?") But sommeliers are very stupid.

BEST MARKET

Quai Saint-Antoine on a Sunday morning. The famous Les Halles de Paul Bocuse is a shopping mall of high-end products, incomprehensible to a non-Lyonnais unless you are an anthropologist studying the Lyonnais psyche as manifest in its irrational habits of food consumption. But for dinner? The Quai.

BEST PLACE TO DRINK IN VIEUX LYON

Le Georges Five, run by the impresario Georges dos Santos (his store, Antic Wines, supplies the good restaurants, where you'll also eat Bob's bread). Georges is at the bar.

WHERE TO SHAKE THE HAND OF GOD, AKA PAUL BOCUSE

At 8am, over coffee with Mère Richard, the cheese lady, at Les Halles de Paul Bocuse. (Like your lentils from Puy, there is one place for cheese.) At 8.30am, over a coffee with Colette Sibilia, the charcuterie lady. (Like your lentils from Puy, etc.) At 10am, over a coffee at Bernachon, the chocolatier. (Lentils, Puy, etc.) For Monsieur Paul, as God is known locally, the mornings are busy (I learned from Blandine Thenet, on my first and last meeting with a Lyonnais publicist), because the afternoons are even busier and when Monsieur Paul heads out to the estate of his mistress, shoots wild animals, has sex, a nap, returns home, bearing rabbits and pheasants, and then, according to Blandine, pops upstairs to have sex with his not-to-be-neglected wife, showers, slips into his chef whites for the evening service of Lyon's only three-star restaurant, his, located downstairs from his home and where you can eat dishes conceived in 1934, 1946, 1958 and 1974, recreated by four MOFs in the kitchen. For a year, I avoided the place, believing it to be a museum. (I was wrong.) Then, I avoided it because I couldn't afford it. (I was right.) Then we ate there: twice. It's kitsch, yes, but unique (what else do you want from a meal?), and flawless: a perfect version of itself. Bocuse is 85.

WHY YOU DON'T KNOW LYON

Because the Lyonnais don't want you to know, and wouldn't know how to tell you, anyway. The dysfunction is expressed in a mini-Eiffel Tower located atop the city's mountain. The city's elders concluded, 120 years ago, that Paris had so many tourists because Paris had an Eiffel Tower. Ergo, what Lyon needed… Today, Lyon still has no tourists. But it now has a tower. Lyon is unusual and seems to be exceptionally incompetent at publicising itself. In fact, it doesn't want visitors. It fears discovery. The Lyonnais: they like their food, they eat it, they talk about it all day long. They don't care what you think about it. They don't care if you like it, if you eat it, if you never even try it. They don't care about you at all.

BUT WHY FRANCE?

Before I arrived, I asked this question. Why France now, when everything groovy is happening somewhere elsewhere? Why France, when even the most chauvinistic members of the most uncompromising Gallic tribe must concede that their claim of making the best food in the world is, for the first time in four centuries, no longer exclusively theirs? Seventeen years ago, Joel Robuchon, then regarded as the best chef in France, declared that Ferran Adrià, the chef of El Bulli in Spain, was even better because Ferran Adrià was "the best cook on the planet", and that statement – Spain hot, France cold – has been repeated ever since: not that French food isn't what it used to be, but that it is what it used to be. After I arrived, I stopped asking the question. Why France? Why not?

WHY STILL HERE?

By chance, we landed on one of those uniquely animated patches of earth that people just don't leave: our quartier, rough, cheap, drunken (by the eternal Rue de Bouteille), violent (three Saturday night deaths in a row), but ancient and alive. Many of the restaurants I've mentioned are here, in our quartier, not least because they get their bread and inspiration from Bob: no one works longer or so uncompromisingly. Bob is in the boulangerie all night on Fridays and Saturdays. I see Bob three times every day, except Wednesdays, the day Bob closes. Wednesdays are a little bit lonely.

On an afternoon in July, I realised that a bakery was, in effect, keeping us in France. It now seems absurd, although it didn't at the time. So I took Bob out to dinner, to celebrate my realisation, and we drank Rhone wines until the early hours of the morning, whereupon I returned home and Bob returned to the bar of Potager (yet another resto worth visiting).

Just before Christmas, my wife and I attended a répas held by Roberto, the owner of another nearby restaurant, on his last night: he had accepted an unexpected offer for his premises. It was a sad-sweet-happy-high-low occasion, just about everyone in the quartier crammed into Roberto's dining room, except Bob, who couldn't get a babysitter. So we didn't see him that night. Then he died. At five that morning. Just like that. It was sudden. It was unexpected. He was 46.

Bill Buford is the author of Heat. He is completing a book about being a French cook, provisionally titled Dirt & Dinner: Hauling my Sorry-ass Family to France for Three Years (and Counting)